It is well-known that the trace-free Einstein tensor of a pseudo-Riemannian metric cannot arise by variation of a local diffeomorphism-invariant action functional with the (inverse) metric as field variable. We show that this statement remains true even for general local actions, without the assumption of diffeomorphism invariance.

We investigate the asymptotic symmetry group of a SU(2)-Yang-Mills theory coupled to a Higgs field in the Hamiltonian formulation. This extends previous work on the asymptotic structure of pure electromagnetism by Henneaux and Troessaert, and on electromagnetism coupled to scalar fields and pure Yang-Mills fields by Tanzi and Giulini. We find that there are no obstructions to global electric and magnetic charges, though that is rather subtle in the magnetic case. Again it is the Hamiltionian implementation of boost symmetries that need a careful and technically subtle discussion of fall-off and parity conditions of all fields involved.

We present a systematic approach to determine all relativistic phases up to $\mathcal{O}(c^{-2})$ in light-pulse atom interferometers in weakly curved spacetime that are based on elastic scattering, namely Bragg diffraction and Bloch oscillations. Our analysis is derived from first principles using the parameterized post-Newtonian formalism. In the treatment developed here, we derive algebraic expressions for relativistic phases for arbitrary interferometer geometries in an automated manner. As case studies, we consider symmetric and antisymmetric Ramsey-Bord\'e interferometers, as well as a symmetric double diffraction interferometer with baseline lengths of 10 m and 100 m. We compare our results to previous calculations conducted for a Mach-Zehnder interferometer.

We consider the Dirac equation coupled to an external electromagnetic field in curved four-dimensional spacetime with a given timelike worldline γ representing a classical clock. We use generalised Fermi normal coordinates in a tubular neighbourhood of γ and expand the Dirac equation up to, and including, the second order in the dimensionless parameter given by the ratio of the geodesic distance to the radii defined by spacetime curvature, linear acceleration of γ , and angular velocity of rotation of the employed spatial reference frame along γ . With respect to the time measured by the clock γ , we compute the Dirac Hamiltonian to that order. On top of this ‘weak-gravity’ expansion we then perform a post-Newtonian expansion up to, and including, the second order of 1/c , corresponding to a ‘slow-velocity’ expansion with respect to γ . As a result of these combined expansions we give the weak-gravity post-Newtonian expression for the Pauli Hamiltonian of a spin-half particle in an external electromagnetic field. This extends and partially corrects recent results from the literature, which we discuss and compare in some detail.

In this contribution we deal with several issues one encounters when trying to couple quantum matter to classical gravitational fields. We start with a general background discussion and then move on to two more technical sections. In the first technical part we consider the question how the Hamiltonian of a composite two-particle system in an external gravitational field can be computed in a systematic post-Newtonian setting without backreaction. This enables us to reliably estimate the consistency and completeness of less systematic and more intuitive approaches that attempt to solve this problem by adding `relativistic effects' by hand. In the second technical part we consider the question of how quantum matter may act as source for classical gravitational fields via the semiclassical Einstein equations. Statements to the effect that this approach is fundamentally inconsistent are critically reviewed.

Space-based research can provide a major leap forward in the study of key open questions in the fundamental physics domain. They include the validity of Einstein’s Equivalence principle, the origin and the nature of dark matter and dark energy, decoherence and collapse models in quantum mechanics, and the physics of quantum many-body systems. Cold-atom sensors and quantum technologies have drastically changed the approach to precision measurements. Atomic clocks and atom interferometers as well as classical and quantum links can be used to measure tiny variations of the space-time metric, elusive accelerations, and faint forces to test our knowledge of the physical laws ruling the Universe. In space, such instruments can benefit from unique conditions that allow improving both their precision and the signal to be measured. In this paper, we discuss the scientific priorities of a space-based research program in fundamental physics.

General Relativity (GR) holds a special place amongst all fundamental theories of physics: on one hand, it is the theory of all gravitational phenomena; on the other hand, it is also a theory of spacetime [...]

In statistical thermodynamics the 2nd law is properly spelled out in terms of conditioned probabilities. As such it makes the statement, that `entropy increases with time' without preferring a time direction. In this paper I try to explain this statement–which is well known since the time of the Ehrenfests–in some detail within a systematic Bayesian approach.

We prove that any $G=SU(2)\times U(1)$ symmetric spacetime that is Ricci flat (i.e. solves the matter-free $\Lambda=0$ Einstein equations) with non-null $G$-orbits is locally isometric to some maximally extended generalised Taub-NUT spacetime.

We investigate the asymptotic symmetry group of a scalar field minimally-coupled to an abelian gauge field using the Hamiltonian formulation. This extends previous work by Henneaux and Troessaert on the pure electromagnetic case. We deal with minimally coupled massive and massless scalar fields and find that they behave differently insofar as the latter do not allow for canonically implemented asymptotic boost symmetries. We also consider the abelian Higgs model and show that its asymptotic canonical symmetries reduce to the Poincaré group in an unproblematic fashion.

This paper deals with the Newton–Wigner position observable for Poincaré-invariant classical systems. We prove an existence and uniqueness theorem for elementary systems that parallels the well-known Newton–Wigner theorem in the quantum context. We also discuss and justify the geometric interpretation of the Newton–Wigner position as `centre of spin', already proposed by Fleming in 1965 again in the quantum context.

In this paper we propose to use Lie sphere geometry as a new tool to systematically construct time-symmetric initial data for a wide variety of generalised black-hole configurations in lattice cosmology. These configurations are iteratively constructed analytically and may have any degree of geometric irregularity. We show that for negligible amounts of dust these solutions are similar to the swiss-cheese models at the moment of maximal expansion. As Lie sphere geometry has so far not received much attention in cosmology, we will devote a large part of this paper to explain its geometric background in a language familiar to general relativists.

In this paper we extend the WKB-like ‘non-relativistic’ expansion of the minimally coupled Klein–Gordon equation after (Kiefer and Singh 1991 Phys. Rev. D 44 1067–76; Lämmerzahl 1995 Phys. Lett. A 203 12–7; Giulini and Großardt 2012 Class. Quantum Grav. 29 215010) to arbitrary order in c−1, leading to Schrödinger equations describing a quantum particle in a general gravitational field, and compare the results with canonical quantisation of a free particle in curved spacetime, following (Wajima et al 1997 Phys. Rev. D 55 1964–70). Furthermore, using a more operator-algebraic approach, the Klein–Gordon equation and the canonical quantisation method are shown to lead to the same results for some special terms in the Hamiltonian describing a single particle in a general stationary spacetime, without any ‘non-relativistic’ expansion.

We extend the systematic calculation of an approximately relativistic Hamiltonian for center of mass and internal dynamics of an electromagnetically bound two-particle system by Sonnleitner and Barnett [Phys. Rev. A 98, 042106 (2018)] to the case including a weak post-Newtonian gravitational background field, described by the Eddington-Robertson parametrized post-Newtonian metric. Starting from a proper relativistic description of the situation, this approach allows us to systematically derive the coupling of the model system to gravity, instead of ``guessing'' it by means of classical notions of relativistic effects. We embed this technical result into a critical discussion concerning the problem of implementing and interpreting general couplings to the gravitational field and the connected problem of how to properly address the question concerning the validity of the Equivalence Principle in Quantum Mechanics.

Building on the work of Giulini and Holzegel (2005 (arXiv:gr-qc/0508070)), a new numerical approach is developed for computing Cauchy data for Einstein's equations by gluing a Schwarzschild end to a Brill–Lindquist metric via a Corvino-type construction. In contrast to, and in extension of, the numerical strategy of Doulis and Rinne (2016 Class. Quantum Grav. 33 075014), the overdetermined Poisson problem resulting from the Brill wave ansatz is decomposed to obtain two uniquely solvable problems. A pseudospectral method and a Newton–Krylov root finder are utilized to perform the gluing. The convergence analysis strongly indicates that the numerical strategy developed here is able to produce highly accurate results. It is observed that Schwarzschild ends of various ADM masses can be glued to the same interior configuration using the same gluing radius.

In this paper we extend the WKB-like ‘ non-relativistic ’ expansion of the minimally coupled Klein – Gordon equation after (Kiefer and Singh 1991 Phys. Rev. D 44 1067 – 76; L ä mmerzahl 1995 Phys. Lett. A 203 12 – 7; Giulini and Gro ß ardt 2012 Class. Quantum Grav. 29 215010) to arbitrary order in c − 1 , leading to Schr ö dinger equations describing a quantum particle in a general gravitational field, and compare the results with canonical quantisation of a free particle in curved spacetime, following (Wajima et al 1997 Phys. Rev. D 55 1964 – 70). Furthermore, using a more operator-algebraic approach, the Klein – Gordon equation and the canonical quantisation method are shown to lead to the same results for some special terms in the Hamiltonian describing a single particle in a general stationary spacetime, without any ‘ non-relativistic ’ expansion.